Question

A conducting circular loop of area 1 mm² is placed coplanarly with a long, straight wire at a distance of 20 cm from it. The straight wire carries an electric current which changes from 10 A to zero in 0.1 s. Find the average emf induced in the loop in 0.1 s.

Answer 1

Given:
Area of the loop, A = 1 mm²
Current through the wire, i = 10 A
Separation between the wire and the loop, d = 20 cm
Time, dt = 0.1 s
The average emf induced in the loop is given by
$$\begin{gathered} e=\frac{\mathrm{d\varphi }}{\mathrm{d}t} \\ =\frac{BA}{\mathrm{d}t}=\frac{{\mu }_{0}i}{2\pi d}\times \frac{A}{\mathrm{d}t} \\ =\frac{4\mathrm{\pi }\times {10}^{-7}\times 10}{2\mathrm{\pi }\times 2\times {10}^{-1}}\times \frac{{10}^{-6}}{1\times {10}^{-1}} \\ =1\times {10}^{-10}\mathrm{V} \end{gathered}$$